MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ's solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This understanding motivates us to design a MINRES-like algorithm to compute minimum-length solutions to singular symmetric systems. MINRES uses QR factors of the tridiagonal matrix from the Lanczos process (where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned systems (singular or not), MINRES-QLP can give more accurate solutions than MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better estimates of the solution and residual norms, the matrix norm, and the condition number.Comment: 26 pages, 6 figure

Mitigating Temporal Misalignment by Discarding Outdated Facts

While large language models are able to retain vast amounts of world knowledge seen during pretraining, such knowledge is prone to going out of date and is nontrivial to update. Furthermore, these models are often used under temporal misalignment, tasked with answering questions about the present, despite having only been trained on data collected in the past. To mitigate the effects of temporal misalignment, we propose fact duration prediction: the task of predicting how long a given fact will remain true. In our experiments, we demonstrate how identifying facts that are prone to rapid change can help models avoid from reciting outdated information and identify which predictions require seeking out up-to-date knowledge sources. We also show how modeling fact duration improves calibration for knowledge-intensive tasks, such as open-retrieval question answering, under temporal misalignment by discarding volatile facts. Our data and code will be released publicly at https://github.com/mikejqzhang/mitigating_misalignment

Chylous Leak During Posterior Approach to Juvenile Scoliosis Surgery: A Case Report.

CaseWe report the first documented case of chylous leak recognized intraoperatively during posterior spinal instrumentation and fusion for juvenile scoliosis in a female patient with a history of thoracotomy and decortication for an empyema.ConclusionsThoracic duct injury can lead to severe morbidity and mortality because of chylothorax formation. Although chylous leaks are a well-documented complication of the anterior approach to spine surgery, leaks during the posterior approach are rarely reported. When these chylous leaks are recognized intraoperatively, the likelihood of serious complications may be minimized by drain placement before closure

Preparing for the Unexpected: Recognizing a Tortuous Thoracic Aorta During Ultrasound-guided Thoracentesis

Ultrasound-guidance has become the standard of care for bedside thoracentesis. This manuscript describes the importance of utilizing point-of-care-ultrasound (POCUS) and color Doppler in avoiding an unusual, but potentially catastrophic aortic puncture during thoracentesis. The case describes a 70 year-old man who presented with one week of shortness of breath. He was found to have a large left-sided pleural effusion on imaging studies. During a bedside POCUS examination, he was found to have a hyperechoic linear structure in his posterior left hemithorax. Ultrasound application of color Doppler revealed a pulsatile flow, confirming visualization of the aorta. The site of needle insertion for thoracentesis was placed more laterally to avoid aortic puncture. The thoracentesis was performed successfully with removal of about 1000ml of sanguinous fluid. This clinical case demonstrates the importance of considering anatomic variants when performing a thoracentesis. As in this patient’s case, ultrasonography and color Doppler during thoracentesis can be useful in avoiding a potentially life-threatening puncture of the aorta

Binary black hole late inspiral: Simulations for gravitational wave observations

Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of General Relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late inspiral stage on orbits with very low eccentricity and evolve for ~1200M through ~7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass ~14 cycles before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to PN calculations for the earlier parts of the inspiral provides a combined waveform with less than half a cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR >~ 10 for some intermediate-mass binary black holes (IMBBHs) out to z ~ 1, and that LISA can see massive binary black holes (MBBHs) in the range 3x10^4 100 out to the earliest epochs of structure formation at z > 15.Comment: 17 pages, 20 figures. Final published versio